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quadric mesh simplification - handle multiple vertex attributes

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I'm implementing 'Quadric-Based Polygonal Surface Simplification' for vertices with multiple attributes (pos, color, uv, etc.).

I am using this thesis as reference: clicky.

So each vertex is a vector of arbitrary dimension (> 3). For normal triangles, I can compute the 'generalized quadric' using the steps given in section 5.2 (generalized error metric) with no problem.

Now I get stuck at the step of calculating the general quadric for the 'constraint plane' described in section 3.6. A constraint plane is a plane perpendicular to the face through an open edge. In 3D, it's easy; but in n-dimension space, how can I form the 'perpendicular' plane and calculate its quadric?

Thanks for help!

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